So this might be a very loaded question. I'd like to build a little robot with a webcam that can do some recognition (i.e., find the red ball, go to the blue square), and was wondering if this was feasible with an arduino. If not, what would be the best way to approach this. I've built a robot before, but it was a simple hexapod with ping sensors, so my coding knowledge is still minimal. Any help or direction would be greatly appreciated, especially if it is something i can do without purchasing new parts. Many thanks to all!

For the image processing part, I'd use OpenCV. That needs far more processing power and resources than the typical Arduino can provide. It doesn't seem to me to be completely impossible that it could be made to run on a Due, but I haven't heard of anyone successfully doing that yet so you'd be blazing the trail - and the answer might be that it isn't possible. Putting the image processing on a PC, on the other hand, is a tried and trusted approach and doesn't involve you solving any hard problems - just getting up to speed on the technology involved.

I only provide help via the forum - please do not contact me for private consultancy.

The main problem is getting the image into the arduino in the first place. A web cam is not the simplest of interfaces to use.What ever you will need a Due as the other arduinos can't do this.

Take a look at the Raspberry Pi, that supports web cams and has lots of memory, it is just that for the robot control bit it is not very real time. So a Pi and and arduino Uno would be a good combination.